Finite Group Databasebeta

← #29700911

Subgroups — #29700911

Order 15616.

860 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C22⋊D61C211yesmaximal, characteristic
2C2×#16839823C211yesmaximal, characteristic, complemented
3#21449076C211yesmaximal, characteristic
4#21446536C211yesmaximal, characteristic, complemented
5#21446433C211yesmaximal, characteristic, complemented
6#21446430C211yesmaximal, characteristic, complemented
7#21446379C211yesmaximal, characteristic, complemented
8#21446374C211yesmaximal, characteristic, complemented
9#21446116C211yesmaximal, characteristic
10#21445998C211yesmaximal, characteristic, complemented
11#21445997C211yesmaximal, characteristic, complemented
12#21445692C211yesmaximal, characteristic, complemented
13#21445600C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1729C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×C4×C22⋊D61C2211yescharacteristic
18C8×C22⋊D61—24no—
19#16839823—24no—
20C2×C4⋊#92418C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519688C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35#16839700C411yescharacteristic
36#16839697C411yescharacteristic
37#16839693C411yescharacteristic
38#16839690C411yescharacteristic
39#16839690C411yescharacteristic
40#16839688C411yescharacteristic
41#16839677C411yescharacteristic
42#16839677C411yescharacteristic
43C4×#11758196C2211yescharacteristic
44C4×#11758196C2211yescharacteristic
45C4×#11758198C2211yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×C22⋊Dic61C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C2×C8×D61—22no—
68C2×C8×D61—22no—
69C2×C8×D61—41no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—22no—
72C2×#11758196C2×C411yescharacteristic
73C2×#11758196C2×C411yescharacteristic
74C2×#11758196C2×C411yescharacteristic
75C2×#11758196C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×C22⋊Dic61C2×C411yescharacteristic
78C2×C22⋊Dic61C2×C411yescharacteristic
79C2×C22⋊Dic61C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C4⋊#92418—22no—
89C4⋊#92418—22no—
90#14519706—22no—
91#14519706—22no—
92#14519706—41no—
93C22⋊#92418—22no—
94C22⋊#92418D414yes—
95#14519689—22no—
96#14519689—22no—
97#14519689—41no—
98#14519688—22no—
99#14519687—22no—
100C4×#92418—22no—
101C8×Dic61—22no—
102C8×Dic61—41no—
103#14519684C2×C411yescharacteristic
104#14519684C2×C411yescharacteristic
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C2×M16×C61—22no—
115C2×M16×C61—22no—
116C2×M16×C61—41no—
117C22×C8×C61—22no—
118C22×C8×C61—22no—
119C22×C8×C61—41no—
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124#117×C61—22no—
125#117×C61—22no—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61C2×C411yescharacteristic
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C24×C61C22×C411yescharacteristic
133C23×D61C22×C411yescharacteristic
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C2×D412yes—
144C22×C4×C61#4112yes—
145C22×C4×C61C2411yescharacteristic
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162M16×C61—44no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—44no—
174C2×C8×C61#4112yes—
175C2×C8×C61#4112yes—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C22⋊C4×C61—22no—
179C22⋊C4×C61—22no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—21no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C22⋊Dic61—41no—
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—41no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418C2×D412yes—
214C2×#92418C2×D412yes—
215C8×D61—44no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61C4×D412yes—
223C23×C61C23×C411yescharacteristic
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61#13112yes—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61C4×D412yes—
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C2×C4×C612−1+411yescharacteristic
256C22⋊D61—28no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61#13112yes—
277C2×Dic61#13112yes—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—41no—
282C8×C61—22no—
283C8×C61—22no—
284C8×C61—41no—
285C8×C61—41no—
286#92418—22no—
287#92418—22no—
288#92418—41no—
289#92418—41no—
290#22901—611nomaximal, Sylow
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—22no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61C2×C4×D411yescharacteristic
299C22×C61C4×#4111yescharacteristic
300C22×C61#52011yescharacteristic
301C22×C61C2×#13111yescharacteristic
302C22×C61C2×#13111yescharacteristic
303C22×C61C2×#13111yescharacteristic
304C22×C61#56811yescharacteristic
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C4×C61—22no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61—41no—
317C4×C61#54611yescharacteristic
318C4×C61#54711yescharacteristic
319C4×C61#55111yescharacteristic
320C4×C61#55211yescharacteristic
321Dic61—22no—
322Dic61—22no—
323Dic61—41no—
324Dic61—41no—
325Dic61—41no—
326Dic61—41no—
327Dic61—41no—
328C2×C8×D4—611no—
329C2×#433—611no—
330#2395—611no—
331#1939—611no—
332#1924—611no—
333#1924—611no—
334#1916—611no—
335#1916—611no—
336#1870—611no—
337#1850—611no—
338#1850—611no—
339#1771—611no—
340#1753—611no—
341C8×C22⋊C4—611no—
342#1729D6111yescharacteristic, complemented
343C2×C61—42no—
344C2×C61#235911yescharacteristic
345C2×C61#292911yescharacteristic
346C2×C61#293511yescharacteristic
347C2×C61#296611yescharacteristic
348C2×C61#296911yescharacteristic
349C2×C61#299211yescharacteristic
350C2×C61#299411yescharacteristic
351D61—42no—
352C22×M16C2×D6111yescharacteristic
353C23×C8—611no—
354C23×C8C2×D6111yescharacteristic
355C2×C4×D4—611no—
356C2×#117C2×D6111yescharacteristic
357C8×D4—1224no—
358#433—1224no—
359C2×C4⋊C8—611no—
360C2×C4⋊C8—611no—
361C2×C4⋊C8—611no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8—611no—
364C2×C22⋊C8—611no—
365C2×C22⋊C8—611no—
366C2×C22⋊C8—611no—
367C2×C22⋊C8—611no—
368C2×C22⋊C8—611no—
369C2×#97—611no—
370C2×#97—611no—
371C2×C4×C8—611no—
372C2×C4×C8—611no—
373C2×C4×C8—611no—
374#400—611no—
375#399—611no—
376#398—611no—
377#397—611no—
378#397—611no—
379#397—611no—
380#394—611no—
381#394—611no—
382C4×C4⋊C4—611no—
383C4×C4⋊C4—611no—
384C4×C22⋊C4—611no—
385C4×C22⋊C4—611no—
386C4×C22⋊C4—611no—
387#336—611no—
388#336—611no—
389#336—611no—
390#336—611no—
391#336—611no—
392#336—611no—
393#336C2×D6111yescharacteristic
394#336C2×D6111yescharacteristic
395#336C2×D6111yescharacteristic
396#336C2×D6111yescharacteristic
397C61#2290111yescharacteristic, complemented, Sylow
398C22×D4—611no—
399C23×C4—611no—
400C23×C4C22×D6111yescharacteristic
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—41no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—41no—
407C22×C8—611no—
408C22×C8—611no—
409C22×C8—611no—
410C22×C8—611no—
411C22×C8—1222no—
412C22×C8—1222no—
413C22×C8—2441no—
414C22×C8C22×D6111yescharacteristic
415C22×C8C22×D6111yescharacteristic
416C22×C8C22×D6111yescharacteristic
417C22×C8C22×D6111yescharacteristic
418C4×D4—1222no—
419C4×D4—1222no—
420#117—22no—
421#117—22no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4C4×D6111yescharacteristic
428C2×C4⋊C4C4×D6111yescharacteristic
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—611no—
433C2×C22⋊C4—611no—
434C2×C22⋊C4—611no—
435C2×C22⋊C4—611no—
436C2×C22⋊C4—611no—
437C2×C22⋊C4C4×D6111yescharacteristic
438C2×C22⋊C4C4×D6111yescharacteristic
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42C22×D6111yescharacteristic
443C2×C42C22×D6111yescharacteristic
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C4⋊C8—2441no—
449C22⋊C8—614no—
450C22⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8—1222no—
453C22⋊C8—2441no—
454#97—1222no—
455#97—1222no—
456C4×C8—1222no—
457C4×C8—1222no—
458C4×C8—2441no—
459#95—611no—
460#95—611no—
461#95—611no—
462#95—611no—
463#95—611no—
464#95—611no—
465#95—611no—
466#95—611no—
467#95—611no—
468#95—611no—
469C24—611no—
470C24C2×C4×D6111yescharacteristic
471C2×D4—1222no—
472C2×D4—1222no—
473C2×D4—1222no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4C2×C4×D6111yescharacteristic
492C22×C4C2×C4×D6111yescharacteristic
493C22×C4C2×C4×D6111yescharacteristic
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C2×C4×D6111yescharacteristic
496C22×C4D4×D6112yes—
497C22×C4#1175822412yes—
498C22×C4C23×D6111yescharacteristic
499M16—44no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—44no—
511C2×C8—612no—
512C2×C8—612no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—2444no—
524C2×C8#1175822212yes—
525C2×C8#1175822212yes—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—1222no—
529C4⋊C4—1222no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—2441no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—2441no—
542C22⋊C4—2441no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C42—1221no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—612no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23—1221no—
564C23—1221no—
565C23—1221no—
566C23#1451973712yes—
567C23C22×C4×D6111yescharacteristic
568D4—1228no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—612no—
588C2×C4—612no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4#1451973712yes—
613C2×C4C2×D4×D6111yescharacteristic
614C2×C4C2×#1175822411yescharacteristic
615C2×C4C2×#1175822211yescharacteristic
616C2×C4C2×#1175822211yescharacteristic
617C2×C4#1451982211yescharacteristic
618C2×C4#1451982511yescharacteristic
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—1222no—
624C8—1222no—
625C8—2441no—
626C8—2441no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—1222no—
635C22—1222no—
636C22—1222no—
637C22—2441no—
638C22—2441no—
639C22—2441no—
640C22—2441no—
641C22C2×#1451973711yescharacteristic
642C22C4×#1175822211yescharacteristic
643C22#1684024311yescharacteristic
644C22#131×D6111yescharacteristic
645C22#131×D6111yescharacteristic
646C22#131×D6111yescharacteristic
647C22#1684052711yescharacteristic
648C4—22no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—1222no—
654C4—1222no—
655C4—2441no—
656C4—2441no—
657C4—2441no—
658C4—2441no—
659C4—2441no—
660C4#1684040211yescharacteristic
661C4#1684041311yescharacteristic
662C4#1684043811yescharacteristic
663C4#1684044711yescharacteristic
664C2—42no—
665C2—2442no—
666C2#2144880711yescharacteristic
667C2#2145451611yescharacteristic
668C2#2145455911yescharacteristic
669C2#2145479011yescharacteristic
670C2#2145481911yescharacteristic
671C2#2145495611yescharacteristic
672C2#2145497711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1729C2
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1729D61
hypocenterC61#22901
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1729

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16839823C2semidirect
4. #21446536C2semidirect
5. #21446433C2semidirect
6. #21446430C2semidirect
7. #21446379C2semidirect
8. #21446374C2semidirect
10. #21445998C2semidirect
11. #21445997C2semidirect
12. #21445692C2semidirect
13. #21445600C2semidirect
14. #21445589C2semidirect
15. C61×#1729C2semidirect
342. #1729D61semidirect
397. C61#22901semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C8×C22⋊D612
C2×#168398232
#214490762
#214465362
#214464332
#214464302
#214463792
#214463742
#214461162
#214459982
#214459972
#214456922
#214456002
#214455892
C61×#17292
#2290161